If a person swim the 50-meter freestyle in 28.12 seconds. This is 0.14 second less than persons previous fastest time is 28.26.
What is Equation?
Two or more expressions with an equal sign is called as equation.
Given that,
One swim the 50-meter freestyle in 28.12 seconds..
The previous fastest time be x.
The new fastest time is 28.12 seconds.
New fastest time is 0.14 second less than your previous fastest time.
So, 28.12+0.14=x
28.26=x
Hence the previous fastest time is 28.26 seconds.
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Clara's suitcase weighs 58 1/4 pounds, but the airline's weight limit for suitcases is 50 pounds. How much weight does she need to remove from her suitcase?
Clara needs to remove 8 1/4 pounds from her suitcase to meet the airline's weight limit.
To find out how much weight Clara needs to remove from her suitcase, we subtract the airline's weight limit from the weight of her suitcase.
First, let's convert 58 1/4 pounds to a proper fraction:
[tex]\[ 58 \frac{1}{4} = \frac{58 \times 4 + 1}{4} = \frac{232 + 1}{4} = \frac{233}{4} \][/tex]
Now, let's subtract the airline's weight limit from Clara's suitcase weight:
[tex]\[ \text{Excess weight} = \frac{233}{4} - 50 \][/tex]
To subtract fractions, we need a common denominator:
[tex]\[ \text{Excess weight} = \frac{233}{4} - \frac{200}{4} \][/tex]
[tex]\[ \text{Excess weight} = \frac{233 - 200}{4} \][/tex]
[tex]\[ \text{Excess weight} = \frac{33}{4} \][/tex]
Now, let's convert this back to a mixed number:
[tex]\[ \text{Excess weight} = 8 \frac{1}{4} \text{ pounds} \][/tex]
So, Clara needs to remove 8 1/4 pounds from her suitcase to meet the airline's weight limit.
A car travels down a highway at 25 m/s. An observer stands 100m from the highway.
a) How fast is the distance from the observer to the car increasing when the car passes in front of the observer?
(Use decimal notation.)
The rate is =
(b) How fast is the distance increasing 10s later?
(Use decimal notation. Give your answer to three decimal places.)
The rate is =
The rate at which the distance from the observer to the car is increasing is 25 m/s, both when the car passes in front of the observer and 10 seconds later.
Explanation:To find the rate at which the distance from the observer to the car is increasing, we need to use the concept of relative velocity. When the car passes in front of the observer, its velocity is perpendicular to the line connecting the observer and the car. Therefore, the rate at which the distance is increasing is equal to the speed of the car. In this case, the rate is 25 m/s.
To find how fast the distance is increasing 10 seconds later, we need to consider the fact that the car is still moving at a constant velocity of 25 m/s. Therefore, the rate at which the distance is increasing remains the same. So, the rate is still 25 m/s.
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A bag of marbles contains 5 red, 3 blue, 2 green, and 2 yellow marbles.What is the probability that you choose a blue marble and then another blue marble, assuming you replace the first marble?
The probability of drawing a blue marble and then another blue marble from a bag, with replacement of the first marble, is calculated by multiplying the probability of the first event by the probability of the second event since the first event's outcome does not change the conditions for the second draw. In this case, the probability is 1/16.
The question involves calculating the probability of drawing two blue marbles consecutively from a bag, with replacement of the first marble before drawing the second one. To find this probability, we calculate the chance of drawing a blue marble twice, taking into account that the composition of the bag remains the same after the first draw due to replacement.
The total number of marbles is 5 red + 3 blue + 2 green + 2 yellow = 12 marbles. The probability of drawing a blue marble is the number of blue marbles divided by the total number of marbles, which is 3/12 or 1/4. Since the first marble is replaced, the probabilities remain the same for the second draw. Therefore, the probability of drawing a blue marble on the second draw is also 1/4.
To find the combined probability of both events happening in succession, we multiply the probabilities of each individual event: (1/4) * (1/4) = 1/16. Thus, the probability of drawing a blue marble and then another blue marble, with replacement, is 1/16.
Raj eats 1/11 of a pound of grapes in 1/25 of a minute. How many minutes will it take him to eat a full pound of grapes?
Solve The Following Question:
5/13t = -9
5/13t=-9
to find t divide both sides by 5/13
t = -9 / 5/13=
-117 /5 =-23.4
t = -23.4
find the next three terms in the geometric sequence: 2, 4, 8, 16
A rancher has 50,000 linear feet of fencing and wants to enclose a rectangular field and then divide it into four equal pastures with three internal fences parallel to one of the rectangular sides. what is the maximum area of each pasture?
Final answer:
To find the maximum area of each pasture, we can create a rectangular field and divide it into four equal pastures. By using the given linear footage of fencing, we can find the dimensions of the rectangular field and calculate the area for each pasture.
Explanation:
To find the maximum area of each pasture, we can start by creating a rectangular field using the given 50,000 linear feet of fencing. Let's consider the length of the rectangular field as 'x' and the width as 'y', with x being the longer side.
The perimeter of the rectangular field is given by 2x + y = 50,000. Since we want to divide the field into four equal pastures, we can divide the rectangular field into four equal widths, with each width being y/4.
Therefore, the area of each pasture is x * (y/4) = (x*y)/4.
To find the maximum area, we can substitute 2x + y = 50,000 into the formula for the area of each pasture. Solving for y in terms of x gives us y = 50,000 - 2x.
Substituting this value of y into the formula for the area, we get A = x * ((50,000 - 2x)/4).
To maximize the area, we can differentiate the area formula with respect to x and set it equal to zero. Solving this equation will give us the value of x that maximizes the area. Once we have that, we can substitute it back into the area formula to find the maximum area of each pasture.
When creating a bar graph to represent data, the researcher used a scale that was too small. The outcome was a graph that appeared to show very little variation. This is a classic example of an error in which phase of inferential statistics? A.data gathering B.data organization C.data analysis D.probability-based inference
The error in using a scale that is too small on a bar graph falls under the data organization phase. This phase involves selecting a scale that accurately represents data without distorting trends or variations.
Explanation:When creating a bar graph to represent data, if the researcher uses a scale that is too small, resulting in a graph that shows very little variation, it is likely an error in the data organization phase. This is because choosing an appropriate scale is a key part of the process of organizing data for visualization. A scale that's too small can compress the data too much and fail to show important differences between data points, while a scale that's too large can exaggerate these differences. In a well-organized graph, the scale should be such that it both accurately represents all the data and makes it easy to identify trends and variations.
It is important to be skeptical of graphs and understand that data organization can have a significant impact on how the information is perceived. A graph is a single visual perspective, and therefore, it is crucial that the scale used does not distort the underlying relationship it is intended to represent. When organizing data in a graph, it's essential to select a scale that neither overshadows nor exaggerates the significant figures and trends of the data points.
Using a scale that is too small in a bar graph is an error in the data organization phase of inferential statistics.
Explanation:The error of using a scale that is too small and resulting in a bar graph that shows very little variation is a classic example of an error in data representation, which falls under the phase of in inferential statistics.
Simplify 3(4x + 6) - 9x.
-15x + 18
3x + 18
3x + 6
12x + 18 - 9x
The expression 3(4x + 6) - 9x simplifies to 3x + 18 by distributing the 3 and then combining like terms.
To simplify the expression 3(4x + 6) - 9x, we need to follow the steps of distribution and then combine like terms.
First, distribute the 3 into the parentheses: 3 * 4x is 12x and 3 * 6 is 18, giving us 12x + 18.Next, subtract the 9x from 12x: 12x - 9x equals 3x.Combine the result with the 18, to end up with the simplified expression 3x + 18.Therefore, the simplified form of 3(4x + 6) - 9x is 3x + 18.
Write in the standard form a+bi (-4+8i)-(7-4i)
which of the following was a result of prison reform during the 1800s
A. a decrease in prisons
B. a decrease in crime
C. the formation of mental hospitals
D. the formation of public schools in rural areas
Answer:
C. the formation of mental hospitals
Step-by-step explanation:
During that time the jail and asylum conditions were worse.
The inmates especially the mentally ill, were bound in chains and locked in cages.
Hence, with the reform movement, came the formation of mental hospitals. Public asylums were made for the mentally ill incarcerated people.
What is the end behavior of f(x)=5x^3-2x+5
Tommy can exchange 8 euros for 11 dollars.
At this rate, how many dollars can Tommy get with 12 euros?
Tommy would be able to get $16.50.
The first step would be to find out the number of dollars you need to exchange for a single Euro.
If 8 Euros go for $11, one Euro would be:
= Amount of dollars / Amount of Euros
= 11 / 8
= $1.375 per Euro
For 12 Euros therefore, the number of dollars Tommy would get is:
= Amount of Euros x conversion factor
= 1.375 x 12
= $16.50
In conclusion, Tommy would get $16.50.
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solve for first two positive solutions sin(3x)cos (4x)+cos(3x)sin(4x)=-0.9
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Marshall bought some pet supplies for $15. The sales tax was 6%. He wrote the expression 1.06(15) to find his total cost.
Which equivalent expression could he also use to find the total cost?
A. 15+0.6(15)
B. (1+0.06)15
C. 1+0.06(15)
D.15 + 0.06
order 40/97,3/41,1/6 from least to greatest
Samantha parents bought her a new bed they paid 136 each month for 9 months how much did the bed cost
Write a number between 1 and 50 that has at least 8 factors. B.) Write the factors.
Answer:
24 has 8 factors with 1,2,3,4,6,8,12,and 24
Step-by-step explanation:
write an expression that shows how to multiply 4 x 362 using place value and expanded form.
To multiply 4 x 362 using place value and expanded form, first expand 362 to (300 + 60 + 2). Then multiply 4 with each value, resulting in 1200, 240, and 8. The sum of these results gives the final answer, 1448.
Explanation:The multiplication expression of 4 x 362 using expanded form and place value can be represented as follows:
Firstly, write 362 in its expanded form. You can express it as (300 + 60 + 2).Then, multiply 4 by each number of the expanded form of 362. The operation would be: 4 x 300 = 1200, 4 x 60 = 240, and 4 x 2 = 8.Finally, add all the resulting numbers together to get the final answer. The operation would be 1200 + 240 + 8 = 1448.
So, 4 multiplied by 362 using place value and expanded form equals to 1448.
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Which number is 100 times greater than 6 thousandths
You deposit $5000 each year into an account earning 8% interest compounded annually. How much will you have in the account in 20 years?
License plates in a particular state display 2 letters followed by 3 numbers. How many different license plates can be manufactured for this state?
In Mathematics, to calculate the number of different license plates with 2 letters followed by 3 numbers, multiply the possibilities for each position: 26 × 26 for letters and 10 × 10 × 10 for numbers to get 676,000 different license plates.
Explanation:The question pertains to the concept of permutations and combinations in Mathematics, specifically calculating the number of different license plates that can be manufactured when the format is two letters followed by three numbers. The number of possible license plates is found by multiplying the number of options for each component. For the letters, there are 26 possible choices for each of the two letter positions (assuming the English alphabet is used and letters can be repeated). For the numbers, there are 10 possible choices for each of the three number positions (using digits 0-9).
To calculate the total number of different license plates, we multiply the possibilities for each part: 26 × 26 × 10 × 10 × 10 = 676,000 different license plates. This calculation is known as the Rule of Product in combinatorics, which states that if one event can occur in 'm' ways and a subsequent event can occur in 'n' ways, then the total number of ways the two events can occur is m × n.
To determine the number of different license plates, multiply the number of alphabetic combinations (26 for each of the 2 letters) by the numeric combinations (10 for each of the 3 numbers), resulting in 676,000 possible plates.
Explanation:The question is asking us to calculate the number of different license plates that can be manufactured with a specific format, which is 2 letters followed by 3 numbers. To solve this, we will assume there are 26 possibilities for each letter (A through Z) and 10 possibilities for each number (0 through 9).
For the two letters at the start, since both positions can hold any of the 26 letters in the alphabet, the total number of combinations for the two letters is 26 × 26.
For the three numbers following, each position can hold any digit from 0 to 9, giving us 10 × 10 × 10 combinations for the numbers.
To find the total number of different license plates, we multiply the number of possibilities for the letters by the number of possibilities for the numbers:
Total license plates = 26 × 26 × 10 × 10 × 10 = 676,000.
Therefore, there can be 676,000 different license plates manufactured for this state with the given format.
Find the height of a door on a scale drawing if the door is 2 meters tall and the scale is 1 centimeter = 4 meters. Round to the nearest tenth.
The height of the door in the drawing will be 1/2 centimeters.
What is scale factor?Scale factor is used to compare the size of two objects. Mathematically, we can write -
{K} = S{O1}/S{O2}
13 mg
Given is that the height of a door on a scale drawing if the door is 2 meters tall and the scale is 1 centimeter = 4 meters.
Height of the door = 2 meters
Scale : 1 centimeter = 4 meters.
So, in one meters, there will be - 1/4 centimeters.
In 2 meters, there will be -
(1/4) x 2 = 1/2 centimeters
Therefore, the height of the door in the drawing will be 1/2 centimeters.
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248mph equals how many meters per second
Every night, Mary spends 3 hours doing homework, 30 minutes practicing the piano, and 35 minutes talking on the phone. What is the total number of minutes Mary spends doing these activities?
The Lombardo family went out to dinner and their full mean costed $62. If they left a 20% tip, how much did they tip?
Which colonial power's policy was based on assimilation of native peoples?
find the equation to the line that is perpendicular to y=2x-3 and goes through the point (-1,2)
Margo borrows $1900, agreeing to pay it back with 6% annual interest after 13 months. How much interest will she pay?
A card is randomly selected from a deck of 52 cards. Find the probability that the card is between four and eight (inclusive) or is a club.
Answer:
20/52+13/52-5/52=.538
Step-by-step explanation:
The probability that the card is between four and eight (inclusive) or is a club is 4/13.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The number of cards can be written as,
The number of cards between 4 and 8 is 3 {4,5,6,7,8}.Number of club cards = 13Number of cards between 4 and 8 from heart, spades, and diamonds = 15Now, the probability that the card is between four and eight (inclusive) or is a club is,
Probability
= (Number of club cards+ Number of cards between 4 and 8)/(Total number of cards)
= (13+15)/(52)
= 28/52
= 4/13
Hence, the probability that the card is between four and eight (inclusive) or is a club is 4/13.
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